Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems
This work addresses the problem of learning low-dimensional representations for complex nonlinear physical systems, which is important for researchers and engineers working with PDEs and mechanical systems.
This paper develops data-driven methods using Variational Autoencoders (VAEs) to learn parsimonious representations of nonlinear systems, specifically those arising from parameterized PDEs and mechanics. The approach incorporates geometric and topological priors through general manifold latent space representations, and its performance is investigated on the nonlinear Burgers equation and constrained mechanical systems.
We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning from observations nonlinear state space models. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.